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A With-In Host Dengue Infection Model with Immune Response and Beddington-DeAngelis Incidence Rate
Department of Mathematics, Sharif University of Technology, Tehran, Iran
Department of Mathematics, Sharif University of Technology, Tehran, Iran
- 1 Department of Mathematics, Sharif University of Technology, Tehran, Iran
- 2 Department of Mathematics, Sharif University of Technology, Tehran, Iran
Applied Mathematics·Volume 03 (2012)·Pages 177–184·Published 23 February 2012·DOI10.4236/am.2012.32028
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Abstract
A model of viral infection of monocytes population by dengue virus is formulated in a system of four ordinary differenttial equations. The model takes into account the immune response and the incidence rate of susceptible and free virus particle as Beddington-DeAngelis functional response. By constructing a block, the global stability of the unin-fected steady state is investigated. This steady state always exists. If this is the only steady state, then it is globally asymptotically stable. If any infected steady state exists, then uninfected steady state is unstable and one of the infected steady states is locally asymptotically stable. These different cases depend on the values of the basic reproduction ratio and the other parameters.
KeywordsWith-In Host ModelDengue Viral InfectionBasic Reproduction RatioBeddington-DeAngelis Immune Response
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